past papers Flashcards
what is a hypothesis
a hypothesis is a statement about a model parameter
Define observed information for 1 single param
What is a sufficient statistic
Def profile likelihood
Def 1 sided hypothesis test
Def marginal likelihood in Bayes theorem
Find minimal sufficient stat
Identity pdf
Identify joint pdf
Apply factorisation theorem (find h(x) that doesn’t depend on θ)
Then for minimal
When finding fisher information remember to
Switch to single variable case
Method of moments
Where moments are acquired/given earlier
Prove consistency
Use LLN (+CMT if necessary)
LLN
Sn
Difference between strong and weak LLN
If mean is finite => weak (converges in P to μ)
If mean AND var is finite => strong (a.s coverages to μ)
Bayes theorem
When determining conjugate prior remember to
Only include the kernel of the distribution
When asked about n -> inf
For bayesian point estimator
Divide through by n to see dominant terms